PAT.1040 Longest Symmetric String(区间dp)

1040 Longest Symmetric String (25分)

 

Given a string, you are supposed to output the length of the longest symmetric sub-string. For example, given Is PAT&TAP symmetric?, the longest symmetric sub-string is s PAT&TAP s, hence you must output 11.

Input Specification:

Each input file contains one test case which gives a non-empty string of length no more than 1000.

Output Specification:

For each test case, simply print the maximum length in a line.

Sample Input:

Is PAT&TAP symmetric?

Sample Output:

11


本题思路：区间dp的思想，不过区间dp一般还枚举区间中间的状态量，而此题由于是回文，当中间不是回文串的时候直接不考虑，中间是回文串则直接长度增加，相对较简单。

当然此题也可以用马拉车和暴力AC。但显得不够优雅/xyx

#include <iostream>
#include <string>
#include <cstring>
using namespace std;

const int maxn = 1000 + 5;

int dp[maxn][maxn];

int main() {
    for(int i = 0; i < maxn; i ++) {
        dp[i][i] = 1;
    }
    string s;
    getline(cin, s);
    int n = s.length();
    int ans = 1;
    for(int len = 1; len < n; len ++) {
        for(int i = 0; i < n - 1; i ++) {
            int j = i + len;
            if(s[i] == s[j]) {
                if(len == 1) {
                    dp[i][j] = 2;
                } else if(dp[i + 1][j - 1] > 0) {
                    dp[i][j] = 2 + dp[i + 1][j - 1];
                }
                ans = max(ans, dp[i][j]);
            }
        }
    }
    cout << ans << endl;
    return 0;
}